2/3y+y-4=30

Solution for 2/3y+y-4=30 equation:

2/3y+y-4=30

We move all terms to the left:

2/3y+y-4-(30)=0


Domain of the equation: 3y!=0

y!=0/3

y!=0

y∈R


We add all the numbers together, and all the variables

y+2/3y-34=0

We multiply all the terms by the denominator


y*3y-34*3y+2=0

Wy multiply elements

3y^2-102y+2=0

a = 3; b = -102; c = +2;
Δ = b2-4ac
Δ = -1022-4·3·2
Δ = 10380
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{10380}=\sqrt{4*2595}=\sqrt{4}*\sqrt{2595}=2\sqrt{2595}$
$y_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-102)-2\sqrt{2595}}{2*3}=\frac{102-2\sqrt{2595}}{6}
$
$y_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-102)+2\sqrt{2595}}{2*3}=\frac{102+2\sqrt{2595}}{6}
$